§ 1.1 Field of the Invention
The present invention concerns correcting integral nonlinearity errors (INL) and/or differential nonlinearity errors (DNL) of multi-bit digital-to-analog converters (DAC). In particular, the present invention concerns employing both a calibration analog-to-digital converter (CADC) to estimate DACs nonlinearity errors, as well as first-order mismatch shaping, such as data-weighted averaging (DWA) for example, in order to further simplify circuit design while increasing the DAC's accuracy.
§ 1.2 Related Art
The use of multi-bit quantizers in delta-sigma modulators has great advantages over single-bit ones, such as increased signal-to-noise ratio (SNR) and improved stability. (See, e.g., S. R. Norsworthy, R. Schreier, and G. C. Temes, Eds., Delta-Sigma Data Converters: Theory, Design, and Simulation, New York: IEEE Press, 1996), referred to as “the Norsworthy paper”).) However, the performance bottleneck is usually the linearity of the internal multi-bit “analog” DAC (ADAC1), which needs to be at least as good as that of the overall converter. This limitation applies for both multi-bit delta-sigma analog-to-digital converters (See FIG. 4.) and digital-to-analog converters (See FIG. 5.). (See, e.g., the Norsworthy paper.)
There are many known techniques to deal with the nonlinearity of the multi-bit ADAC in delta-sigma modulators. Dynamic element matching, also called mismatch shaping (See, e.g., the Norsworthy paper; L. R. Carley, “A noise-shaping coder topology for 15+ bit converters,” IEEE Journal of Solid-State Circuits, vol. SC-24, no. 4, pp. 267-263, April 1989; B. H. Leung and S. Sutaija, “Multi-bit sigma-delta A/D converter incorporating a novel class of dynamic element matching techniques,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, vol. 39, no. 1, pp. 35-51, January 1992 (referred to as “the Leung paper”); R. T. Baird and T. S. Fiez, “Linearity enhancement of multibit delta-sigma A/D and D/A converters using data weighted averaging,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, vol. 42, no. 12, pp. 753-761, December 1995 (“the Baird paper”); R. Schreier and B. Zhang, “Noise-shaped multi-bit D/A converter employing unit elements,” IEE Electronics Letters, vol. 31, no. 20, pp. 1712-1713, 1995 (“the Schreier paper”); T. Kwan, R. Adams, and R. Libert, “A stereo multibit sigma-delta DAC with asynchronous master-clock interface,” IEEE Journal of Solid-State Circuits, vol. 37, no. 12, pp. 1881-1887, December 1996 (“the Kwan paper”); and I. Galton, “Spectral shaping of circuit errors in digital-to-analog converters,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, vol. 44, no. 10, pp. 808-817, October 1997 (“the Galton paper”).) transforms harmonic distortion into shaped pseudo-random noise, which is usually acceptable in the output. There are several methods that can achieve first-order shaping such as individual-level averaging (See the Leung and Baird papers), vector feedback (See the Schreier paper.), butterfly structures (See the Kwan paper.), selection trees (See the Galton paper), etc.
However, first-order methods require relatively high values (e.g., 16 or higher) of the over-sampling ratio (OSR) to be effective. Therefore, second-order mismatch shaping techniques were developed. (See the Schreier and Galton papers.)
However, second-order methods need increased circuit complexity, which increases power consumption and requires a large integrated chip area. In addition to dynamic element matching, off-line correction (See, e.g., M. Sarhang-Nejad and G. C. Temes, “A high-resolution multibit sigma-delta ADC with digital correction and relaxed amplifier requirements,” IEEE Journal of Solid-State Circuits, vol. 28, no. 6, pp. 648-660, June 1993), and on-line correction (See, e.g., C. Petrie and M. Miller, “A background calibration technique for multibit delta-sigma modulators,” in Proceedings of the IEEE International Symposium on Circuits and Systems, May 2000, vol. 2, pp. II.29-II.32; and X. Wang, P. Kiss, U. Moon, J. Steensgaard, and G. C. Temes, “Digital estimation and correction of DAC errors in multibit delta-sigma ADCs,” IEE Electronics Letters, vol. 37, no. 7, pp. 414-415, 29 Mar. 2001).), digital calibration, as well as on-line analog correction (See, e.g., U. Moon, J. Silva, J. Steensgaard, and G. C. Temes, “A switched-capacitor DAC with analog mismatch correction,” IEE Electronics Letters, vol. 35, no. 22, pp. 1903-1904, October 1999).), correction have been used. An on-line digital linearizing technique for ADACs embedded into pipelined ADCs, based on correlation operations, was also discussed. (See, e.g., I. Galton, “Digital cancellation of D/A converter noise in pipelined A/D converters,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, vol. 47, no. 3, pp. 185-196, March 2000).
It was shown recently that multi-bit error-feedback (EF) modulators can use aggressive noise-transfer functions (NTF) without compromising stability and can therefore, achieve high resolution even for low (e.g., 4 or 8) OSR values. (See, e.g., P. Kiss, J. Arias, and D. Li, “Stable high-order delta-sigma digital-to-analog converters,” IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 51, no. 1, pp. 200-205, January 2004 (referred to as “the Kiss paper”), and See especially FIG. 6.) Unfortunately the EF topology is not suitable for delta-sigma ADCs since the imperfections of the analog loop filter H(z) would enter the critical input node and adversely affect the output. However, this drawback does not exist in digital modulator loops. Therefore, EF modulators are widely used in delta-sigma DACs. (See, e.g., U.S. Pat. No. 4,467,316 to H. G. Musmann and W. Korte, titled “Generalized interpolative method for digital/analog conversion of PCM signals”; and P. J. Naus, E. C. Dijkmans, E. F. Stikvoort, A. J. McKnight, D. J. Holland, and W. Bradinal, “A CMOS stereo 16-bit D/A converter for digital audio,” IEEE Journal of Solid-State Circuits, vol. 22, no. 3, pp. 390-395, June 1987.), and fractional-N PLLs (See, e.g., S. Willingham, M. Perrott, B. Setterberg, A. Grzegorek, and B. McFarland, “An integrated 2.5 GHz delta-sigma frequency synthesizer with 5 μs settling and 2 Mb/s closed loop modulation,” in IEEE International Solid-State Circuits Conference, Digest of Technical Papers, February 2000, pp. 200-201.).
A 4th-order 5-bit EF DAC was proposed in the Kiss paper which used an aggressive NTF. Since only 10-bit signal-to-noise-and-distortion ratio (SNDR) was targeted at an OSR of 4, using DWA was sufficient to handle the 5-bit ADAC's nonlinearity. The same 4th-order 5-bit EF DAC can potentially achieve 14 bits of resolution (88.9-dB SNR) for an OSR of 8. This accuracy, however, cannot be achieved with DWA (alone) at such a low OSR.
In view of the foregoing it would be useful to improve the correction of errors in digital filters including an analog digital-to-analog converter.